相关论文: A Topological Application of Labelled Natural Dedu…
Topological self-stabilization describes the ability of a distributed system to let the nodes themselves establish a meaningful overlay network. Independent from the initial network topology, the system converges to the desired topology via…
When an image classifier outputs a wrong class label, it can be helpful to see what changes in the image would lead to a correct classification. This is the aim of algorithms generating counterfactual explanations. However, there is no…
We give an exposition of Natural Topology (NToP), which highlights its advantages for exact computation. The NToP-definition of the real numbers (and continuous real functions) matches recent expert recommendations for exact real…
We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed…
Topological transforms have been very useful in statistical analysis of shapes or surfaces without restrictions that the shapes are diffeomorphic and requiring the estimation of correspondence maps. In this paper we introduce two…
We present a tableau calculus for reasoning in fragments of natural language. We focus on the problem of pronoun resolution and the way in which it complicates automated theorem proving for natural language processing. A method for…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node…
Correctness of program transformations in extended lambda calculi with a contextual semantics is usually based on reasoning about the operational semantics which is a rewrite semantics. A successful approach to proving correctness is the…
Path calculus, or graphical linear algebra, is a string diagram calculus for the category of matrices over a base ring. It is the usual string diagram calculus for a symmetric monoidal category, where the monoidal product is the direct sum…
We present an abstract unifying framework for interpreting Stone-type dualities; several known dualities are seen to be instances of just one topos-theoretic phenomenon, and new dualities are introduced. In fact, infinitely many new…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
We introduce the calculus of Classical Transitions (CT), which extends the research line on the relationship between linear logic and processes to labelled transitions. The key twist from previous work is registering parallelism in typing…
We define and study a term calculus implementing higher-order node replication. It is used to specify two different (weak) evaluation strategies: call-by-name and fully lazy call-by-need, that are shown to be observationally equivalent by…
Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
Linear type systems need to keep track of how programs use their resources. The standard approach is to use context splits specifying how resources are (disjointly) split across subterms. In this approach, context splits redundantly echo…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
Modeling distributed computing in a way enabling the use of formal methods is a challenge that has been approached from different angles, among which two techniques emerged at the turn of the century: protocol complexes, and directed…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
In this article we propose an extension to the typed natural deduction calculus TNDPQ to model verification of counterfactual fairness in probabilistic classifiers. This is obtained formulating specific structural conditions for causal…